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Mach, Ernst

Mach, Ernst

(b. Chirlitz-Turas near Brno, Moravia [now Chrlice-Tuřany, Czechoslovakia], 18 February 1838; d. Vaterstetten, near Haar, Germany, 19 February 1916)

physics, physiology, psychology.

Ernst Mach spent his entire life, until the final three years, in the Austro-Hungarian empire. It was a time of increasing national self-determination, affirmations of linguistic identity among the non-Germanic peoples, and physical and intellectual emancipation of various ethnic groups. His parents provided an environment which nurtured unrestrained, critical, and stubborn scientific inquisitiveness and skepticism.

Mach was the first of three children of Johann Mach and Josephine Lanhaus. His father had received an excellent classical education that included two years’ study in the philosophy faculty of the University of Prague. In 1840 he settled with his family on a farm in Untersiebenbrunn, near Vienna. Johann Mach was a practical and inventive idealist, a stark individualist who, with the collaboration of members of his more or less secluded household, distributed his efforts between improving methods of silkworm cultivation, tending his orchard, observing behavior in animals and children, reading Greek and Latin classics, and private tutoring. Mach’s mother was raised within the tradition of a family engaged in law and medicine. She was a woman of tender character and artistic disposition, absorbed in instilling in her children a love of music and poetry.

Except for a year at the Benedictine Gymnasium in Seitenstetten, Mach was instructed at home by his father until he was fourteen. In 1848, at age ten, a year that remained fixed in Mach’s memory as one dominated by parental sympathies for the Hungarian revolution against the Hapsburg monarchy, he entered the first class of the Gymnasium. He enjoyed the geography lessons, but he was so turned away by the grammar of ancient languages and pious aphorisms that his religious mentor recommended a handicraft or career in business for the untalented student. Accordingly, Mach’s father again assumed the supervision of the boy’s education. The mornings were taken up with studies in the prescribed Gymnasium subjects—Greek and Latin grammar and literature, history, algebra, and geometry—liberally punctuated with observational and experimental interludes in house, garden, and woods. The afternoons were devoted in part to manual labor in the father’s agricultural ventures and in part to an apprenticeship with a cabinetmaker.

Mach entered the sixth class of the public Piarist Gymnasium in Kremsier (Kroměříž) in 1853 at the age of fifteen. The religious exercises displeased him but were more than compensated for by his enthusiasm for the way in which the natural sciences were presented. In later years Mach at various times paid special tribute to his teacher of natural history and geography, F. X. Wessely. Apparently Wessely presented Lamarck’s theory of evolution (before Darwin’s Origin of Species was published) so convincingly that Mach never managed to rid himself of an underlying evolutionary epistemology grounded in an appeal to the inheritance of acquired characteristics.

After five years of mathematics, physics, and philosophy at the University of Vienna, in 1860 Mach received the doctorate with a dissertation on electrical discharge and induction. While at the university, working as a Privatdozent in the laboratory of his teacher, Andreas von Ettingshausen (Doppler’s successor in the chair of physics), Mach carried out a series of experimental investigations designed to provide theoretical support for Doppler’s controversial law relating changes of musical pitch and optical frequency to the relative motion of signal and receiver. Furthermore, he presented a number of papers to the Academy of Sciences in Vienna in which he employed the idea of intermolecular vibrations to account for gaseous spectra, “Molecular functions” was the term Mach used to explain the phenomena of resonance in mechanically vibrating systems, the behavior of fluids in relation to density and viscosity, capillary phenomena, and the principal radii of curvature of liquid surfaces.

Although Mach derived most of his income in Vienna from popular scientific lectures on optics, musical acoustics, and psychophysics, he also presented formal university lectures on the principles of mechanics and designed a special course in physics for medical students. The latter formed the basis for his Compendium der Physik für Mediciner (1863). This work notably demonstrated that early in his career Mach had adopted a thoroughly mechanistic interpretation of natural phenomena and accepted the atomic-molecular theory and the kinetic theory of gases without reservation— at least as a working model and hypothesis.1 In this instance Mach simply was following the philosophically atomistic account of physics that was then in fashion among physicists. Even so, in the preface and at the end of the Compendium, Mach explicitly discusses the inadequacies of the atomic theory. He remarks there that whatever metaphysical conception of matter may be put forward in future, the results obtained according to the atomic theory will always be capable of being translated into another conception— just as formulas in polar coordinates may be expressed in rectangular coordinates.

Before leaving Vienna Mach’ scientific interests had begun to shift from physics to the physiology and psychology of sensation and to the new discipline of psychophysics. In the reflections on his life that appear in his Leitgedanken (1910) Mach says that he was pressed into the field of the psychology of sensation because he lacked the means for physical investigations. “Here, where I could observe my sensations, and against their environmental circumstances, I attained, as I believe, a natural Weltanschauung freed from speculative, metaphysical ingredients.”2 When Mach began to explore psychophysical problems associated with vision, audition, and variations in blood pressure, he gradually but surely reached the conclusion that his mechanistic and atomistic approach had netted him very little. This reorientation of Mach’s scientific attention is manifestly visible in the “Vorträge über Psychophysik” that appeared toward the end of 1863. For him this shift represented an escape from metaphysical questions, a retreat from mechanism and physical reductionism, and the intentional avoidance of hypotheses. He wrote: “For the value of a hypothesis consists mainly herein, that by a kind of regula falsi it always leads closer and closer to the truth.”3 By 1863 the atomic hypothesis was already for Mach a kind of regula falsi.

In 1864 Mach accepted a full professorship in mathematics at the University of Graz. Having received no promise of an institute or resources for scientific equipment, he used his own funds to secure the necessary research facilities. By 1866 he was given the title of professor of physics, although he continued to pursue physiological and psychophysical problems on aural accommodation, the sense of time, and spatial vision. Most important at this juncture was Mach’s discovery of what later came to be known as Mach’s bands, a phenomenon that relates the physiological effect of spatially distributed light stimuli to visual perception. A Mach band is observed when a spatial distribution of light results in a sharp change in illumination at some point. A negative change corresponds to a band brighter than its surroundings in the region of sharp change. A positive change corresponds to a band darker than its surroundings in the region of sharp change. This phenomenon, a physiological effect that has no physical basis, was the subject of five papers published between 1865 and 1868. A final paper appeared in 1906. The effect was essentially rediscovered in the I950’s and since has been the subject of considerable investigation.4

In 1867 Mach married Ludovica Marussig in Graz. He had already accepted the professorship of experimental physics at Charles University in Prague. He produced most of his important work during the twenty-eight years he spent in that chair and saw the publication of over a hundred scientific papers. Although he was deeply involved throughout in the theoretical reformation of his views on mechanics and thermodynamics, his journal publications chiefly reflect his experimental endeavors.

Prominent among the psychophysical investigations during the Prague years are Mach’s studies on the changes of kinesthetic sensation and equilibrium associated with physical movement, acceleration, and change of orientation in the human body. To these may be added a steady stream of research papers in which Mach resolutely continued to probe problems already initiated in Vienna and Graz: experiments with spatially distributed retinal stimuli (Mach bands), monocular stereoscopy, the anatomy and function of the organs of auditory perception, and aural accommodation.

Within the discipline of physics proper Mach’s output was no less impressive. The more conventional physical studies carried out in Prague conspicuously include a great variety of optical experiments connected with refraction, interference, polarization, and spectra. He investigated the wave motion associated with mechanical, electrical, and optical phenomena and notably clarified the longitudinal-wave propulsion characteristics of stretched and unstretched glass rods and quartz rods. He also studied the mechanical effects resulting from spark discharge within solids and on surfaces.

Between 1873 and 1893 Mach and various collaborators, including his son Ludwig, devised and perfected optical and photographic techniques to study sound waves and the wave propulsion and gas dynamics of projectiles, meteorites, explosions, and gas jets. Stimulated by the remarks of the Belgian artillerist Henri Melsens, in 1881 Mach undertook to study the flight of projectiles by means of photographic techniques that he had already devised for other experiments in his Prague laboratory.5 His celebrated 1887 paper on supersonics was published jointly with P. Salcher of the Marine Academy of Fiume (now Rijeka, Yugoslavia) in the Sitzungsberichte of the Academy of Sciences in Vienna.6 The experiments described in this classic paper were carried out in Fiume with the support of the Royal Austrian Navy. In this paper, the angle α, which the shock wave surrounding the envelope of an advancing gas cone makes with the direction of its motion, was shown to be related to the velocity of sound ν and the velocity of the projectoe ω as sin α = ν/ω when ω > ν. After 1907, following the work of Ludwig Prandtl at the Kaiser Wilhelm Institut für Strömungsforschung in Göttingen, the angle α was called the Mach angle.7

Recognizing that the value of ω/ν (the ratio of the speed of an object to the speed of sound in the undisturbed medium in which the object is traveling) was becoming increasingly significant in aerodynamics for high-speed projectile studies, J. Ackeret in his inaugural lecture in 1929 as Privatdozent at the Eidgenössische Technische Hochschule, Zürich, suggested the term “Mach number” for this ratio.8 The Mach number was introduced into the literature in English by the late 1930’s and since the end of World War II has taken on considerable importance in theoretical and fluid dynamics. The work that has come to be most closely associated with Mach represents, in all probability, contributions that Mach would have conceived to be almost inconsequential when compared with his criticisms of classical mechanics and his experimental innovations in psychophysiology.

Mach also published while in Prague numerous popular scientific lectures and essays of historical and educational import and major treatises and monographs on conservation of energy (1872), spectral and stroboscopic investigations of musical tones (1873), the theory of the sensation of motion (1875), a critical history of mechanics (1883), and a volume on the analysis of sensations (1886). From 1882 to 1884 he was rector of the university during the difficult days when it separated into a German and a Czech faculty. In 1887 Mach and Johann Odstrcil published, with the help of a number of collaborators, the first of a series of physics textbooks, which ran to some twenty editions and were used with varying success in Germany and Austria for about four decades. Similarly, demonstration apparatus designed in Mach’s laboratory was in use in Prague, Vienna, and Leipzig.

In 1895 Mach moved to the University of Vienna to assume a teaching position in philosophy, with the title professor of the history and theory of the inductive sciences. His Popular Scientific Lectures,, a later edition of which was dedicated to William James, was first published in English in 1895. His Principien dcr Wärmelehre, dedicated to J. B. Stallo, appeared in 1896. In 1897 Mach suffered a stroke which left the right side of his body paralyzed. After a period of recuperation, he resumed lecturing and writing. He officially retired from his professorship in 1901, the year of his appointment to the upper chamber of the Austrian parliament. His Erkenntnis und Irrtum appeared in 1905 and his Space and Geometry in 1906.

In 1913 Mach moved with his wife to the country home of his son Ludwig in Vaterstetten, Germany. His Kultur und Mechanik was published in 1915, the year before he died. Mach’s Die Principien der physikalischen Optik, was published posthumously in 1921.

A physicist by training, Mach wished to be recognized as such. All the same, he was deeply engaged for most of his life in investigating problems in physiology, psychology, and the history and philosophy of science. An overall examination of his lifework reveals that he was an inventive experimentalist, an acute and imaginative critic of scientific theory, and was unusually sensitive to the importance of formulating problems in areas where physics, physiology, and psychology intersect. Mach’s broad fascination with the phenomenal world of his immediate environment was leavened with an unusual and solicitous curiosity about nature in its pristine form. He recognized a strong desire for self-enlightenment and realized that he wanted to be a physicist, but a physicist unconstrained by the conventional barriers of the specialists with whom he came in contact.

In Einstein’s obituary for Mach in 1916 we read: “The unmediated pleasure of seeing and understanding, Spinoza’s amor dei intellectualisextraordinary experimental , was so strongly predominant in him that to a ripe old age he peered into the world with the inquisitive eyes of a carefree child taking delight in the understanding of relationships.”9 Einstein believed that even in those cases in which Mach’s scientific inquiries were not founded on new principles, his work at all times displayed “extraordinary experimental talent”. Even where Mach”s philosophy intruded upon his science his colleagues nevertheless praised his intuition and skill in scientific research. Tn 1927 Wilhelm Ostwald wrote: “So clear and calculated a thinker as Ernst Mach was regarded as a visionary[Phantast], and it was not conceivable that a man who understood how to produce such good experimental work would want to practice nonsense[Allotria]which was so suspicious philosophically.”10 Arnold Sommerfeld spoke of Mach as a brilliant experimentalist but a peculiar theoretician who, in seeking to embrace the “physiological” and “psychical” in his physics, had to relegate the “physical” to a less pretentious level than physicists were accustomed to expect from a colleague.11

Fundamental among Mach’s theoretical contributions and reflections were his explanations of visual, aural, and kinesthetic sensation; his views on mechanics, thermodynamics, optics, and molecular spectroscopy; and the ideas associated with his wave propulsion studies. Generally speaking, at least during his lifetime, Mach’s theoretical opinions were judged to be amalgamated with too many hypercritical, obstreperous, and extrascientific remarks. In other instances, either the subject matter of his inquiries or his approach to the problems, or both, were too far afield to interest professional physicists. Mach’s uncompromising rejection of the atomic theory, for example, far surpassed that of his contempories who, even when noncommittal about atoms and molecules as existential entities, never questioned its extraordinary usefulness as a powerful hypothesis. Mach became less denunciatory about the theory as he became older, but it is doubtful that he ever abandoned his dogmatic antiatomistic position, even after the discoveries at the turn of the century had furnished rather convincing evidence that he was wrong.

Mach looked upon the atomic theory and “the artificial hypothetical atoms and molecules of physics and chemistry” as “traditional intellectual implements” of the discipline. He wrote: “The value of these implements for their special, limited purposes is not one whit destroyed. As before, they remain economical ways of symbolizing experience. But we have as little right to expect from them, as from the symbols of algebra, more than we have put into them, and certainly not more enlightenment than from experience itself.”12

The most severe critic of Mach’s position on thermodynamics was Max Planck,13 for whom the principle of conservation of energy was a true law of nature, a reality independent of man’s existence. For Mach the principle took the position of a maxim or convention for organizing a large class of natural phenomena and was rooted in an anthropomorphic sanction related to a biologically determined economy of effort conducive to survival. “Energy” was for Mach no more than a plausible and powerful concept like force, space, or temperature. Thus it is wrong to include Mach among energeticists such as Wilhelm Ostwald and Georg Helm-as is often done.14

As for the second law of thermodynamics, Boltzmann felt that neither Planck nor Mach had penetrated its statistical essence. After 1900 Planck, but not Mach, accepted Boltzmann’s interpretation. In fact, Mach continued to challenge, on philosophical grounds, the atomic-molecular-mechanical explanation of the laws of thermodynamics, preferring characteristically to give them a more simple and purely postulational status.15 In his Wärmelehre (1896) Mach stated,

The mechanical conception of the Second Law through the distinction between ordered and unordered motion, through the establishment of a parallel between the increase of entropy and the increase of unordered motion at the expense of ordered, seems quite artificial. If one realizes that a real analogy of the entropy increasein a purely mechanical system consisting of absolutely elastic atoms does not exist, one can hardly help thinking that a violation of the Second Law-and without the help of any demon-would have to be possible if such a mechanical system were the real foundation of thermal processes. Here i agree with F. Wald completely, when he says “In my opinion the roots of this (entropy) law lie much deeper, and if success were achieved in bringing about agreement between the molecular hypothesis and the entropy law, this would be fortunate for the hypothesis, but not for the entropy law.”16

While thermodynamics at present enjoys autonomy as a discipline independent of mechanics, at the beginning of the century the statistical interpretation thoroughly permeated thermodynamics because of the great achievements and general reception of the atomic-molecular theory, It is thus even more difficult today to see how Mach could have been so blind to the steady advance of what became one of the most powerful theories for all of the physical sciences,

Mach’s critical reflections on mechanics gave rise to a spirited discussion of the scientific, historical, and philosophical foundations of classical physics. His perspicuity in these matters is admirably demonstrated by the richness of the responses elicited from Hertz, Pearson, Boltzmann, Föppl, Love, Stallo, Clifford, Picard, Poincaré, Duhem, Seeliger, Vailati, and Jourdain. Even so, as Einstein wrote in 1916, referring to Mach’s Die Mechanik of 1883, “There you will find set forth brilliantly ideas which by no means as yet have become the common property of physicists.”17

According to Mach, Newton possessed the two characteristics necessary for greatness in a scientist: an imaginative grasp of the essential elements of experience of the world and the intellectual power of generalization. In Die Mechanik, Mach presented Newton’s mechanical views in considerable detail. He offered generous praise for the clarity of presentation of the Principia along with some forceful arguments for the rational reformulation of some of its concepts. A case in point was Mach’s conception of inertial mass, which he treated not as an intrinsic property of an object but as an entity specified by the dynamical coupling between the object and the rest of the universe. He proposed that Newton’s conception of mass, as quantity of matter, be replaced by an “arbitrarily established definition,” namely, that “all I those bodies are bodies of equal mass, which, mutually acting on each other, produce in each other equal and opposite accelerations.”18 Such a definition, Mach contended, would render superfluous Newton’s special enunciation of the principle of reaction, a conclusion favored for reasons of economy of thought.

Newton’s views on absolute time, space, and motion were challenged in Die Mechanik on the grounds that they could in no way be related to experimental observations, Mach suggested the elimination of all propositions from which observables cannot be deduced and further proposed that the motions of bodies be considered relative to all observable matter in the universe at large; “When we reflect that we cannot abolish isolated bodies…, that is, cannot determine by experiment whether the part they play is fundamental or collateral, that hitherto they have been the sole and only competent means of the orientation of motions and of the descriptions of mechanical facts, then it will be found expedient provisionally to regard all motions as determined by these bodies.”19 On Mach’ terms a body in an empty universe has no inertia. The inertia of a system is reduced to a functional relationship between the system and the rest of the universe, including the most distant parts of the interacting material system.

To call attention to this principle, Einstein, in a four-page paper on general relativity (1918), introduced the expression “Mach principle” (Machsches Prinzip) to emphasize a generalization of Mach’s claim that the inertia of an isolated body can have no meaning;20 that inertia must be reduced to the reciprocal action of bodies; that the inertia frame is determined by the mass distribution in the universe; and that the inertial force on a body is the interaction of distant matter on the body. What is entailed is the choice, even if it be provisional, of a material system that mathematically approximates absolute space.

Mach’ critique of Newtonian mechanics, interpreted by Einstein within the context of Riemannian field theory, served as one of the strongest incentives for the development of Einstein’s gravitational theory—although Einstein eventually discovered that the Mach principle did not hold for his new theory. What it did show was that the metric of space-time could be determined by the distribution of matter and energy; that the curvature of space, and from this the motion of bodies, could be determined from matter in space. Thus the motion of bodies was seen to be due to the influence of the surrounding masses (including the stars) and not, as Newton had supposed, to any effort on the part of bodies to maintain their direction of motion in absolute space.

Mach’s critique of Newtonian mechanics, interpreted by Einstein within the context of Reiemannian field theory, served as one of the strongest incentives for the development of Einstein’s gravitational theory—although Einstein eventually discovered that the Mach principal did not hold for his new theory. What it did show was that the metric of space-time could be determined by the distribution of matter and energy; that the curvature of space, and from this the motion of bodies, could be determined from matter in space. Thus the motion of bodies was seen to be due to the influence of the surrounding masses (including the stars) and not, as Newton had supposed, to any effort on the part of bodies to maintain their direction of motion in absolute space.

Einstein hoped that he would be able to give mathematical expression to the Mach principle; admittedly he was not completely successful. He found support for the Mach principle by showing that his field equations turned out to have no solution, no metric, in matter-free space. He managed to assimilate the reconcilable aspect of Mach’s principle into the general theory of relativity, based on the equivalence principle and the conception of covariance under general transformations of space-time coordinates, but he was not content to accept the qualification of restriction to finite space-time boundary conditions that is implied in the Mach principle. In fact, he discovered that he could write field equations that gave the correct solutions only by adding the so-called cosmological term.21

The scientific and philosophical literature on the reinterpretations and formulations of the Mach principle is huge.22 Demonstrations of its compatibility with gravitational theory and other cosmological models continue to be proposed, reformulated, and rejected. Attempts to show where the principle does or does not make sense continue; as do objections to the principle itself or to parts of a particular formulation of it. Suffice it to say that there is little agreement on the mathematical formulation of the Mach principle. The expression is highly anachronistic as a collective term and has little in common with Mach’s original conception of the problem. Still, the logical connection between Mach’s views on mechanics and Einstein’s theory of relativity, even now, is not a meaningless issue.

In his Autobiographical Notes (1946) Einstein saw “Mach’s greatness in his incorruptible skepticism and independence.” Although he there referred to Mach’s epistemological position as one “which today appears to me to be essentially untenable,’ he also recognized that Mach had influenced his thought during his early years.23 Einstein on several occasions mentioned that he had drawn inspiration from Mach’s Mechanik, and it is therefore something of an enigma that Mach so categorically rejected the theory of relativity. In the preface to Die Principien der physikalischen Optik, written in 1913 but not published until 1921, Mach complained that he was “gradually becoming regarded as the forerunner of relativity” and that philosophers and physicists were carrying on a crusade against him: “I have repeatedly observed that I was merely an unprejudiced rambler, endowed with original ideas, in various fields of knowledge. I must, however, as assuredly disclaim to be a forerunner of the relativists as I withhold from the atomistic belief of the present day. The reason why, and the extent to which, I reject the present-day relativity theory, which I find to be growing more and more dogmatical, together with the particular reasons which have led me to such a view—the considerations based on the physiology of the senses, the theoretical ideas, and above ail the conceptions resulting from my experiments—must remain to be treated in the sequel.”24 The sequel— apparently an attack on Einstein’s theory of relativity -—never materialized.

In considering Mach’s contribution to the history of science, it is helpful to understand that all of his historicocritical writings lend strength to the thesis that the history of a scientific discipline, concept, or theory was for him a means to interpret and illuminate epistemological problems in the philosophy of science that puzzled him as a physicist.25 Mach never undertook to write history with the intent merely of reconstituting the development of the subject as an end in itself. He wrote no history of areas in which he recognized no problem. By the same token he made no attempt to treat any aspect of the history of science in a systematic fashion. He was not predisposed to examine the nature of scientific revolutions or to relate science to its organizational, institutional, or sociocultural framework. He put forward no systematic philosophy of science.

As a young man Mach was given to considerable introspection and puzzlement about the nature of physics and the obligations of the physicist toward the new branches of science opening up alongside physics. By means of historical studies and the critical examination of the foundations of physics, he hoped to achieve insights into the direction that his own work might take. Mach’s writings exerted considerable influence on late nineteenth- and early twentieth-century philosophic thought. The characteristic epistemological questions that Mach formulated were the outgrowth of his preoccupation with physics as seen from within the context of an obstinate inquisitiveness concerning the historical tradition inherited by physics.

Mach was first attracted to the history of science for what it might teach him about physics. In Die Mechanik he spelled this out, saying that

… not only a knowledge of the ideas that have been accepted and cultivated by subsequent teachers is necessary for the historical understanding of a science, but also … the rejected and transient thoughts of the inquirers, nay even apparently erroneous notions, may be very important and very instructive. The historical investigation of the development of a science is most needful, lest the principles treasured up in it become a system of half-understood prescripts, or worse, a system of prejudices. Historical investigation not only promotes the understanding of that which now is, but also brings new possibilities before us, by showing that which exists to be in great measure conventional and accidental. From the higher point of view at which different paths of thought converge we may look about us with freer vision and discover routes before unknown.26

Mach’s historical perspective was biased toward the investigation of specific problems and concepts. To this end, history was not conceived chronologically, biographically, or even topically. The documents that formed the basis of his historical analyses were almost exclusively limited to scientific writings. There is ample evidence that Mach had a good command of Latin, Greek, French, Italian, and English and that the examined the primary sources. In addition he was familiar with a very broad secondary literature and, as his personal correspondence shows, exchanged ideas with an international group of scholars.

In 1863 Mach was already persuaded that his scientific curiosity might be nurtured by a serious study of the history of science, if only as an aid in the teaching of science. For he believed that students should not be expected to adopt propositions as self-evident which had developed over several thousand years. In his first major historical work, Die Geschichte und die Wurzel des Satzes von der Erhaltung der Arbeit (1872), he conjectured that there is “only one way to [scientific] enlightenment: historical studies!” The investigation of nature, he believed, should be founded on a special classical education that “consists in the knowledge of the historical development … of science.” It was not the logical analysis of science but the history of science that would encourage the scientist to tackle problems without engendering an aversion to them. The scientist might follow two paths in order to become reconciled with reality: “Either one grows accustomed to the puzzles and they trouble one no more, or more learns to understand them with the help of history and to consider them calmly from that point of view.”27

The youthful considerations included in the small (fifty-eight-page) Geschichte und Wurzel touched upon themes and points of view that continued to be explored by Mach for the rest of his life: the meaning and function of scientific theories, the epistemological importance of the physiology and psychology of sensation for the natural sciences in general, the principle of economy of thought, the inadequacy of Newtonian mechanics, the sterility of the atomic theory, and the sharp criticism of classical causality, physical reductionism, mechanism, materialism, and all forms of metaphysical speculation. In his historicocritical treatises on mechanics, optics, and heat theory, and in his Analyse der Empfindungen (1886) and Erkenntnis und Irrtum (1905), Mach returned to these same issues. It is instructive to try to identify some of the recurrent themes and cardinal epistemological questions raised in these works and then to discover how they are formulated within the context of Mach’s historical outlook.

The pivotal questions that Mach’s historicocritical analyses sought to elucidate may be formulated as follows: How did we inherit our current scientific concepts and theories? Why are they given to us in the way that we have become accustomed to accpet them, rather than in some other form that may be logically more plausible or aesthetically more commendable? What factors can we identify as contributory to the adoption of preferred modes of reasoning and analogical adaptation from other domains? At any given in history, what was considered to constitute evidence, verification, or a conclusive proof for a scientific theory?

With these questions, formulated and elucidated with examples drawn from the history of science, the essential framework of Mach’s conception of the scientific enterprise takes on a fairly predictable form: Physics comprises only a small part of the body of scientific knowledge: its intellectual concepts and implements are too specialized. The natural sciences are inexpressibly richer than physics, and their history is inexhaustibly diversified. In any particular science that is being actively cultivated the ideas are generally undergoing metamorphosis. Since scientific concepts, laws, and theories are to some extent perennially obsolete, it is meaningless to harp on their anchored truty status. The conceptual creations of science, always tentative and at best incomplete, take on a configuration at any time that reveals the attendant historical circumstances and the convergence of interest and attention of those scientific investigators at work on the problems-now physicists, now physiologists, now psychologists.

Implied here is the notion that the nature and form given to a scientific construct depend in large part on the whims of history and on the environmentally conditioned process of cognitive organization employed by scientists. The concept of matter, for example, is seen to be bound, in its content, to a particular historically determined state of scientific development rather than to any fixed reality. Necessarily subjoined to this cognitive activity-biologically joined, in fact-is a mandate for abstraction and the exercise of economy of thought. Given that there exists no conceivable rock bottom of information potentially relevant for understanding the ways of nature, and recognizing the many alternatives for relating and organizing the facts, the scientific investigator has no choice but to fall back on drastic abstraction and generalization.

Mach, of course, understood that scientists commonly strive to achieve logical consistency, simplicity and elegance of formulation, inclusiveness, and range of applicability. Actually scientific concepts, laws, and hypotheses, when studied within the context of their genesis, do not display so prominently the elegant logical traits and clear features that characterize the orthodox image of science. Instead, their most visible feature is their scientific extrinsicness. With the passage of time, that which is historically acquired comes to be philosophically affirmed. Mach underlined the need for scientists to acknowledge and neutralize the subtle way in which scientific constructs take on a status of philosophical necessity rather than historical contingency.

In Die Mechanik, for example, Mach sought to demonstrate how the historical study of the development of the principles of statics and dynamics—from historical contingency to philosophical necessity—could furnish the tactics for developing the analytical and methodological desiderata for interpreting and purifying the conceptual components of science. By means of the critical, historical, and psychological exposure of the roots of science, Mach intended, above all, to expose metaphysical obscurities, inherited anthropomorphisms, and ambiguities and to demonstrate the artificiality of the mechanical interpretation of the sciences. To this end he explored the function of instinctive knowledge, the role of memory, the correlation between the origin of an idea and its status in science at a given time, the psychology of discovery in contradistinction to the logic of discovery, and the authority that induction and deduction derive from experience.

The disclosure of the mental steps of proof adopted by different investigators is informative. For what reason, by what authority, did Stevin in his consideration of the principle of the inclined plane (based on the condition of equilibrium of an endless uniform chain on a triangular prism) argue from the general to the specific case? Why did Archimedes, on the other hand, in his treatment of the principle of the lever argue from the specific to the general case? What constituted proof is by no means unambiguously clear in these two cases.

Again, when Daniel Bernoulli purported to have demonstrated that the proposition for composition of forces is a geometrical truth independent of experience, Mach accepted this “proof” as no more than a dubious reduction of what is easier to observe from what is more obscure and difficult to observe, a demonstration in which it is possible to conceal the nature of the so-called proof. The significant feature in this case, as Mach saw it, was to search for the historical reasons why Bernoulli’s demonstration might have been accepted as proof. Was it not the case, here as in other examples, that the investigator had built his demonstration on an appeal to instinctive knowledge that is supposed to be self-evident and that claims to be basically different from experiential knowledge? For Mach so-called instinctive knowledge, no matter how heuristically valuable, was assumed to contain important element of experience hidden in its premises. He tried, wherever possible, to buttress this experience-oriented point of view with examples drawn from the history of science.

Mach’s overall objective, narrow as it may seem, was to rid science of concepts that have no parallel in experience. This emphasis frequently has been characterized in the literature as the “Mach criterion,” according to which only those propositions from which statements about observable phenomena can be deduced should be employed in theory. Scientific “proofs” that are not tied to experience, Mach felt, serve either as a cover-up for counterfeit rigor or as an appeal to the so-called higher authority of purely instinctive cognitions. In the case of a family of mechanical principles (exclusion of the perpetuum mobile, center of gravity, virtual work, vis viva, d’Alembert’s principle, Gauss’s principle of least constraint, Maupertuis’s principle of least action, Hamilton’s principle) Mach demonstrated to his own satisfaction that each of these can be derived from any other—given sufficient mathematical ingenuity and perseverance.

Clearly, Mach reasoned, these principles are all related in such a way that, if any one is taken to be true, then all the rest can be deduced by mathematical and logical reasoning. But what affords the rationale for accepting any specific principle as true in the first place? It can only be that the principle provides the right answers to problems in statics and dynamics. If any one of the above principles can be translated by deduction into any other, it nevertheless remains to be shown how the validity of at least one of them can be established, Mach’s answer, given historically, was that the roots of the most primitive of such principles derive from experience. An example might be the experimental impossibility of designing a machine that furnishes unlimited quantities of mechanical work without the input of effort. Mach was dogmatic about this point—that the behavior of nature cannot be divined exclusively on the basis of so-called self-evident suppositions, unless the suppositions are themselves drawn from experience.

Mach analyzed at some length the history of the treatment of problems in statics (using both static and dynamic arguments) and in dynamics (using both dynamic and static arguments). Mach found that, historically considered, statics was prior to dynamics; whereas logically or conceptually understood, statics could be reduced to a limiting case of dynamics. Mach hoped in this way to discover by analysis what clear meaning, if any, was to be attached to the statement that one scientific principle is more fundamental than another. The wider generality of one principle compared to another, Mach felt, was not necessarily a sufficient warrant to accept it as more basic. Nor should the historical priority of discovery or enunciation of one principle over that of an alternative formulation dictate logical status. In short, “basic” and “fundamental” had for Mach no fixed significance when severed from the context of the scientific problem. The practical solution to understanding mechanical principles, Mach felt, was to learn by experience in scientific problem solving.28

Mach’s emphasis in Die Mechanik is neatly summarized as follows:

The most important result of our reflections is …that precisely the apparently simplest mechanical theorems are of a very complicated nature; that they are founded on incomplete experiences, even on experiences that never can be fully completed; that in view of the tolerable stability of our environment they are, in fact, practically safeguarded to serve as the foundation of mathematical deduction; but that they by ho means themselves can be regarded as mathematically established truths, but only as theorems that not only admit of constant control by experience but actually require it.29

Mach’s position on mechanics was an ambiguous one. On the one hand he played upon the crucial importance of a critical analysis of physical principles. On the other hand, he concluded that from a logical, economical, and practical point of view there is no persuasive rationale for defending either the historical legacy or the relevance of mechanics for the development of other scientific disciplines. While the study of the history of science abundantly demonstrates the prestigious place of mechanics, Mach conjectured that its applicability for other scientific domains was severely limited. While mechanics, Mach thought, offered little means of understanding heat theory, electricity, and light, its application within psychology was unqualifiably pernicious. The resolute thrust that haracterized Mach’s efforts to exploit experimental physiology and psychology—in part, by means of physical techniques—was indicative of the genuineness with which he was searching for novel problems and perspectives beyond the conventional physics of his day, without ever being able to relinquish his hold on professional physics or to put aside experimental physics as such.

Mach’s philosophy of science was governed by the impulse to explore in depth the epistemological roots of science; but he was certain that this exploration could not be undertaken by examining the scientist’s work without analyzing his behavior. Hence we recognize Mach’s perseverance in demonstrating the relevance of the analysis of sensations and of the importance of psychology and physiology as a corrective to the prevailing mechanistic physicalism. Mach’s philosophical point of view and, in particular, his emphasis on scientific laws as summary statements of observation led to his being identified with the positivists. In 1909 Lenin published, in Moscow, his Materializm i empirio-kritisizm. Kriticheskie zametki ob odnoy reaktsiomwy filosofii (“Materialism and Empirio-Criticism; Critical Comments on a Reactionary Philosophy”). In this work—much commented upon since then and essential in the development of Soviet Marxism—Lenin scathingly denounced the young Machists. Along with Mach, Avenarius, and Berkeley, they were accused of supporting a pernicious positivism and subjective idealism antithetical to Marxist dialectial materialism.

In addition to being associated with radical and empirical skepticism, positivism, subjective idealism, and the renunciation of truth in any transcendental sense, Mach is known to have supported a theory of knowledge based on the study of biological behavior. The ideas presented in Mach’s Beiträge zur Analyse der Empfindungen (1886; rev. ed., 1900) sprang from the profound conviction, as explained in the preface, “that the foundations of science as a whole, and of physics in general, await their next greatest elucidations from the side of biology, and especially from the an analysis of sensations.”30

In the various revisions of this work, the 1901 edition of which was dedicated to Pearson, Mach explicitly clarified his views on how psychological, physiological, and physical experience, taken as sensations, provide man’s sole source of knowledge concerning the world. The so-called elements of sensation that Mach had in mind—colors, sounds, temperatures, pressures, spaces, times, and so forth— are functionally connected in many ways and are associated with mind, feelings, and volition. Some of these associations (adaptations) stand forth more prominently than others, are engraved on our memory, and are expressed in language. Phenomena are represented as a complex of interrelated sensations embracing the object and subject of the sensations, the sensed, and the senser, such that any dualism between subject and object disappears.

The elements of sensation are not entirely independent, but for the sake of analysis can be separated into three groups-FP The external (äussere) elements, A, B, C, characterize physical bodies and define the discipline of physics; the internal (innere) elements K, L, M, … characterize human bodies and define the discipline of physiology; the interior (innerste) α,β,γ,…,elements, characterize our ego (memory, volitions) and define the discipline of psychology. Since the properties of one and the same physical object, therefore, appear modified and conditioned by our own bodies, our sense organs under different circumstances produce different sensations and perceptions. The gulf that separates physical from psychological investigation resides not in a difference of subject matter but in different modes of investigation in the two domains. For example, to refer to that which is physical in an object being examined is but to designate one method of cognitive organization of which there are many. It is not the facts but the points of view that distinguish the disciplines.

From a psychophysiological point of view, the process of cognition includes the adaptation of thoughts to facts (Beohachiung) and thoughts to other thoughts (Theorie), Mach asserted that the world of the percipent is composed entirely of sensations and not any illusive, protean, pseudophilosophical, Kantian Ding-an-sich that is supposed to remain after all of the qualities of a body are taken from it. Things, bodies, matter—the so-called objects of our experience—are thought symbols for combinations of elements and complexes of sensations and therefore are nothing apart from the totality of their attributes. A more or less complete description of phenomena should be accompanied by a more or less complete statement of the relevant functional relationships. To suit his purposes an investigator can analyze that which is given in experience, but he cannot by any manipulation of the empirically given data produce new information about how nature will behave in a new situation. He can, of course, predict how nature will behave in the empirically unknown, but it is always experience that serves as final judge about how nature in fact does behave in the unknown.

Mach’s so-called principle of psychophysical parallelism as a guide in the investigation of sensations follows from the assumption that all sensations can be investigated from the point of view of physics, physiology, or psychology. There are no sensations uniquely physical or physiological or psychological. There are only sensations to be investigated from different points of view and according to the choice of connections between elements isolated for examination

To strengthen his principle of psychophysical parallelism and to encourage the broadest possible interchange within the physical and biological field, Mach condoned the use of provisional teleological motives because of their heuristic value in formulating significant questions. More important for Mach’s doctrine of how sensations become the basis for behavior or action are his views on biological evolution. He was convinced that all of science had its origins in the needs of life. The animal body is a I relatively constant sum of touch and sight sensations, and all physical knowledge can only mentally represent and anticipate compounds of the elements of sensation.

Mach’s argument can be briefly reconstructed as follows: The external phenomenal world is hopelessly heterogeneous and complex. Biological organisms cannot adapt to this environment, cannot survive, unless the given heterogeneous sensations as stimuli are converted into some focused form of homogeneous behavior that favors self-preservation. Over long periods of lime biological organisms have developed a mechanism of accepting (scanning, rejecting) heterogeneous stimuli and correlating them and integrating them into homogeneous, purposeful behavior. How? By a sensor mechanism—tactile, aural, thermal—that excites but one nerve path; this in turn connects with the brain and gives rise to voluntary and, by habituation, involuntary behavior. The net process from unorganized stimuli to anatomically and symmetrically organized response (an example is the need for rapid locomotion) is a movement toward the biological organism’s evolutionary acquisition of control over nature’s stimuli.

It might be suggested that Mach’s principle of economy of thought was also rooted in evolutionary arguments that championed those survival acts that relate to minimizing effort. Mach’s views on Denkökonomie were first spelled out in his 1868 lecture on “The Form of Liquids” and in Die Ge-schichte und die Wurzel (1872). In the former he compared the principle of least surface for liquids to the miserly but intelligent mercantilist principle of a tailor working with the greatest saving of material, adding: “But why, tell me, should science be ashamed of such a principle? Is science … as a maximum or minimum problem … itself anything more than—a business? Is not its task to acquire with the least possible work, in the least possible time, with the least possible thought, the greatest possible part of eternal truth?”31 Elsewhere, in his 1882 lecture “On the Economical Nature of Physical Inquiry” and in a special chapter in Die Mechanik, Mach reiterated and reemphasized the principle of Denkokonomie and its connection with mathematical reasoning, causality, teleology, evolution, and psychic phenomena.32 The transparent omnipresence of this principle in Mach’s writings led Peirce to say, “Dr. Ernst Mach who has one of the best faults a philosopher can have, that of riding his horse to death, does just this with his principle of Economy in science.”33

As a physicist given to championing psycho-physiology as the science of the future, Mach was not at all persuasive in his obscure position. Was he suggesting that concepts, methods, and distinctive points of view within the domain of psychophysiology might prove effective for investigating problems in the physical sciences that had hitherto been the exclusive concern of professionals in the discipline? Or should the fields of psychology and physiology and their attendant problems be opened up for investigation by the methods developed within the physical sciences? The former position, a rather radical one, catls for an extraordinarily sweeping psychophysiological reconstruction of physical principles—whatever that might entail. The second position, psychology as auxiliary to physics, either approximates physical reduetionism, toward which Mach was ill-disposed, or else borders on psychophysics in the style of Fechner, whose approach considerably influenced Mach. In any case, Mach apparently chose to exploit either possibility, as the occasion demanded; psycho-physiology to provide new directives for physics, and physics enriched through the focus of attention on psychophysiological problems. He seems to have leaned philosophically toward the former but to have organized his own research according to the latter.

While Mach made no claim to be a philosopher, much has been written about his scientific philosophy; he was more of a scientist’s philosopher than a philosopher’s philosopher. In 1886 he wrote in his Analysis of Sensations, “I make no pretension to the title of philosopher. I only seek to adopt in physics a point of view that need not be changed immediately I on glancing over into the domain of another science; for, ultimately, all must form one whole.”34

In the preface to Erkenntnis and Irrtum (1905) Mach remarked that the scientist, without claiming to be a philosopher, has a strong urge to satisfy an almost insatiable curiosity about the origins, structure, process, and conceptual roots of science. Averse to being labeled a philosopher, Mach nevertheless was not timid about raising and discussing methodological and epistemological questions. His progressive drift from physics to the philosophy of science via the history of science is nowhere more clearly evident than in Erkenntnis und Irrtum. The most comprehensive analytical and systematic treatment of Mach’s philosophical views, the work is seldom read and almost never cited by historians of science. When his critics referred to his writings as die Philosophies he replied:

Above all there is no Machist philosophy. At most [there is] a scientific methodology and a psychology of knowledge [Erkenntnispsychologie]; and like all scientific theories both are provisional and imperfect efforts. I am not responsible for the philosophy which can be constructed from these with the help of extraneous ingredients….The land of the transcendental is closed to me. And if I make the open confession that its inhabitants are not able at all to excite my curiosity, then you may estimate the wide abyss that exists between me and many philosophers. For this reason I already have declared explicitly that I am by no means a philosopher, but only a scientist. If nevertheless occasionally, and in a somewhat noisy way, I have been listed among the former then I am not responsible for this. Of course, I also do not want to be a scientist who blindly entrusts himself to the guidance of a single philosopher in the way that Moliere’s physician I expected and demanded of his patients.35

In 1872 Mach wrote, “The object of science is the connection of phenomena; but the theories are like dry leaves which fall away when they have long ceased to be the lungs of the tree of science,”36 Science was for Mach primarily “the compendious representation of the actual.” It is on this crucial point that his thought exhibits a gross miscalculation about the I strength and reach, especially within recent science, of the highly artificial conceptual tools that scientists employ in their exploration of nature and even more of the exploration of that aspect of nature that is a product of the scientists’ own creation.

Superimposed on Mach’s ambitious program to relate the sciences to their historical and philosophical implications was his unflinching drive to unmask the theological, animistic, and metaphysical elements of science as he saw them. For this reason (among others that touch upon the long-range implications of his antirealtstic, anticausal, antimechanisttc, anti-materialistic, and antiatomistic world view) it was virtually impossible for contemporary scientists, philosophers, and historians to avoid taking sides vis-à-vis Mach. Positions of neutrality or indifference were rare during his lifetime—and still are. The deeper he delved into his historical studies the more he became engulfed by philosophical questions. Much as he eschewed the title of philosopher, his involvement with such questions ultimately forced him to carve out a scientific metaphysics of his own—although he would have denied that.

If at times Mach’s historical position and emphasis seem superficial, erroneous, and misdirected, the caliber and import of his work can still be evaluated against the state of the art of historical and philosophical discussions in the sciences in his day.

As Einstein wrote, in the year of Mach’s death, “I even believe that those who consider themselves to be adversaries of Mach scarcely know how much of Mach’s outlook they have, so to speak, absorbed with their mothers’ milk.”37


1. Erwin Hiebert, “The Genesis of Mach’s Early Views on Atomism,” in R. S. Cohen and R. J. Seeger, eds., Ernst Mack; Physicist and Phihsoplier (1970), 79–106.

2. “Die Leiigedanken …,” in Sdentia, 8 (1910), 234.

3. “Aus Dr. Mach’s Vorträgen über Psychophysik,” in Österreichische Zeitschrift für praktische Heilkunde, 9 (1863), 366.

4. Ratliff, Mach Bands: Quantitative Studies on Neural Netwarks in the Retina (1965).

5. Cf, Mach’s 1897 lecture: “On Some Phenomena Attending the Flight of Projectiles,” in Popular Scientific Lectures(1943).

6. E. Mach and P. Salcher, “Photographische Fixirung der durch Projectile in der Luft eingeleiteten Vorgänge,” in Sitzungsberichte der Akadetmie der Wissenschaften in Wien, 95 (1887), 764–780. This paper and four others are conveniently reproduced in Joachim Thiele, ed., Ernst Mach. Arbeiten über Erscheinungen an fliegenden Projectilen (Hamburg, 1966).

7. Ludwig Prandtl, “Neue Untersuchungen über die strömende Bewegung der Gase und Dämpfe,” in Physikalische Zeitschrift, 8 (1907), 23–30.

8. J. Ackeret, “Der Luftwiderstand bei sehr grossen Geschwindigkeiten,” in Schweizerische Bauzeitung, 94 (1929), 179–183.

9. Albert Einstein, “Ernst Mach,” in Physikalische Zeitschrift, 17 (1916), 101–104.

10. Wilhelm Ostwald, Lebenslinien, Eine Selbstbiographie, II (Berlin, 1927), 171.

11. Arnold Sommerfeld, “Nekrolog auf Ernst Mach,” in Jahrbuch der bayerischen Akademie der Wissenschaften (1917), 58–67.

12.Beiträge (1886), pp. 142–143; English ed. (1959), p. 311.

13. For a discussion and evaluation of the differences in philosophical outlook between Mach and Planck, see Erwin Hiebert (1968).

14. Cf. Erwin Hiebert, “The Energetics Controversy and the New Thermodynamics,” in Duane H. D. Roller, ed., Perspectives in the History of Science and Technology (Norman, Okla., 1971), 67–86.

15. Cf. Hiebert, The Conception of Thermodynamics in the Scientific Thought of Mach and Planck (Freiburg im Breisgau, 1968), pp. 104–107.

16.Wärmelehre (1896), p. 364.

17. Einstein, loc. cit. (1916), p. 102.

18.Die Mechanik (1889), p. 203; English ed. (1960), p. 266.

19.Ibid,, pp. 215–216 and 283 resp.

20. Albert Einstein, “Prinzipielles zur allgemeinen Relativitätstheorie,” in Annalen der Physik, 4th ser., 55 (1918), 241–244.

21. See Dictionary of Scientific Biography, IV, 312–333.

22. Cf. Hong-Yee Chiu and W. F. Hoffmann, Gravitation and Relativity (New York, 1964).

23. P. A, Schilpp, ed., Albert Einstein: Philosopher-Scientist (Evanston, III., 1949), p. 21.

24.Die Principien der physikalischen Optik (1921), pp. viii-ix; English ed. (1926), p. vii-viii. See also Joseph Petzoldt, “Das Verhältnis der Machschen Gedankenwelt zur Relativitätstheorie,” in the 8th ed. (1921) of Die Mechanik; and Ludwig Mach’s pref. to the 9th ed. (1933).

25. Cf. Erwin Hiebert, “Mach’s Philosophical Use of the History of Science,” in Roger H. Stuewer, ed,, Historical and Philosophical Perspectives of Science (Minneapolis, 1970), pp. 184–203.

26.Die Mechanik (1889), pp. 237–238; English ed. (1960), pp. 316 317.

27.Geschichte und Wurzel (1872), pp. 1–4; English ed, (1911), pp. 15–18.

28. For Mach’s conception of the role of physical experiments and thought experiments in scientific problem solving, see Erwin Hiebert, “Mach’s Conception of Thought Experiments in the Natural Sciences,” in S. Sambursky Symposium (in press).

29.Die Mechanik (1889), pp. 221–222; English ed. (1960), pp. 289–290.

30.Beiträge (1886), p. v; English ed. (1959), pp. xxxv-xxxvi.

31.Popular Scientific Lectures (1943), p. 16.

32.Ibid. (1943), pp. 186–213; and “Die Oekonomie der Wissenschaft,” in Die Mechanik (1889), pp. 452–466; English ed. (1960), pp. 577–595.

33.Collected Papers of Charles Sanders Peirce, C. Hartschorne and P. Weiss, eds., I (Cambridge, 1931), par. 122,

34.Beiträge (1886), p. 21; English ed. (1959), p. 30.

35.Erkermtnis and Irrtum (1905), pp. vii-viii.

36.Geschichte und Wurzel (1872), p. 46; English ed. (1911), p. 74.

37. Albert Einstein, “Ernst Mach,” in Physikalische Zeitschrift, 17 (1916), 102.


I. Original Works. There is no collected edition of Mach’s works. The Royal Society Catalogue of Scientific Papers lists 91 papers to the year 1900; Poggcndorr is useful but incomplete. The most complete Mach bibliography, for both original works and secondary literature is Joachim Thiele, “Ernst Mach—Bibliographie,” in Centaurus, 8 (1963), 189–237. The section on original works in this bibliography (without the list of secondary works) was revised and updated in Thiele (see below).

The library of the Ernst-Mach-Institut der Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung, Freiburg im Breisgau, owns the largest collection of correspondence and other Mach documents; about 2,500 letters (mostly addressed to Mach) dated 1860-1916, some MSS, and other personalia and information by and about family members. The institute also houses a large but far from complete collection of Mach’s publications and related secondary literature. Other major repositories for Mach correspondence and documents are the Morris Library of Southern Illinois University, Carbondale, 111.; the Burndy Library, Norwalk, Conn.; the Akademie-Archiv of the Deutsche Akademie der Wissenschaften zu Berlin; and the University Library of the Technische Univcrsität, Berlin-Charlottenburg.

The following chronological list of Mach’s published books does not duplicate separately published pamphlets and lectures contained in those volumes.

1. Compendium der Physik für Mediciner (Vienna, 1863).

2. Einleitimg in die Hehnhohz’sche Musiktheorie. Populär für Musiker dargestellt (Graz, 1866).

3. Die Gesehichte und die Wurzel des Satzes von der Erhahung der Arbeit (Prague, 1872), includes Mach’s “Ueber die Definition der Masse,” in Repertorium fiir physikaiische Technik, 4 (1868), 355–359. 2nd ed. (Leipzig, 1909) unchanged except for added ’’Bemerkungen zum zweiten Abdruck,” pp. 59–60. English trans, and annotations by Philip E. B. Jourdain (Chicago-London), 1911.

4. Optisch-akMtische Versuche, Die spectrale and stroboskopische Untersuchung tönender Körper (Prague, 1873).

5. Grundlinien der Lehre von den Bewegungsempfindungen (Leipzig, 1875); facs. ed. (Amsterdam, 1967).

6. Die Mechanik in ihrer Entwickelung historisch-kirtisch dargestellt (Leipzing, 1883). The 8th ed. (1921) includes Joseph Petzoldt, “Das verhältnis der Machschen Geankenwelt zur Relativitätstheorie.” The 9th ed. (1933) contains a pref. by Ludwig Mach; facs. (Darmstadt, 1963). Enghlish trans. of 9th German ed. by Thomas J.McCormack (Chicago-La Slaae, III., 1942). 6th American ed., withnew intro. by Karl Menger (La Salle, III., 1960).

7. Beiträge zur Analyse der Empfindungen (Jena, 1886); 2nd ed., rev. and enl., Die Analyse der Empfindungen und das Verhältnis des Physischen zum Psychischen(Jena, 1900); 9th ed., 1922. English trans. of the 1st German ed. by C.M.Williams (Chichgo. 1897); rev. and supp. from the 5th German ed. by Sidney Waterlow (Chicago, 1914). Paperback ed., with new intro. by Thomas S.Szasz (New York, 1959).

8. Popular Scientific Lectrues, Thomas J.McCormack, trans. (La Salle, III., 1895); 5th ed., 1943.Populärwissenschaftliche Voresugen(Leipzing, 1896), 5th ed., 1923.

9. Die Pricipien der Wärmelehre.Historisch-kritisch entwickelt(Leipzig, 1896); 4th ed., with added index of persons, 1923. No known translaions to date.

10. Erkenntnis und Irrtum. Skizzen zur Psychologie der Forchung (Leipzing, 1905); 2en ed., 1906. The 3rd (1917) through 5th (1926) eds. contain Friedrich Jodl, “Ernst Mach und seine neueste Arbeit: Erkenntnis und Irrtum,” from Neue Freie Presse, 24 Sept. 1905. English trans. in process for Vienna Circle Collection to be published by D.Reidel with intro. and commentary by E.Hiebert.

11. Space and Geometry in the light of Physiological, Psychological and Physical Inquiry, repr. from Monist (La Salle, III., 1906; 1960).

12. kultur und Mechanik(Stuttgart, 1915).

13. Die Leitgedanken meiner naturwissenschaftlichen Erkenntnislehre und ihre Aufnahme durch die Zeitgenossen. Sinnliche Elemente und naturwissenschaftliche Begriffe(Leipzing, 1919), a pamphlet repr. of two essas originally published in Scientia, 8 (1910), 227–240; and pflugers Archiv fiir die gesamte Pysiologie des Menshen und der Tiere,136 (1910), 263–274.

14.Die Principien der physikalischen Optik. Historisch und erkenntnis-psychologisch entwickelt(leipzig, 1921). English trans. by John S.Anderson aand A.F.A.Young (London, 1926; London-New York, 1956).

15. Grundriss der Natrurlehre für die unteren Classen der Mittelschulen(Prague, 1887), written with Johann Odsrčil. Reissued (1887–1913) by Mach, K.Habart and G.wenzwel in various eds. specifically designed for secondary school instruction in Austria and Germany.

16.Grundriss der Physik für die höheren Schulen des Deutschen Reiches(Leipzig, 1890), edited with the help of F.Harbordt and M.Fischer.

17. Leitfaden der Physik für Studierende(PragueVienna-Leipzig, 1891), written with G.Jaumann. 2nd ed., 1891.

II. Secondery Literature.

1. [Maria Mach],Erinnerungen einer Erziehein Nach Aufzichnungen von ***, mit einem Vorwort herausgegeben von Professor Ernst Mach, 2nd ed. (Vienna, 1913). Maria Mach was Ernst Mach’ sister.

2. Friedrich Herneck, “Ueber eine unveroffentliche unveröffentliche Selbstbiographie Ernst Machs,”in Wissenschaftliche Zeitschrift der Humboldt-Universität Berlin, Math.-nat. Reihe, 6 (1956–1957), 209–220, from a thirteen-page MS of 1913 in the achives of the Deutsche Akademie der Wissenschaften zu Berlin.

3.Joachim Thiele, Die Bedeutung Ernst Machs für die Wende von der klassischen zur moderner Physik. Ein Beitrag zur vergleichenden Geschichte wissenchaftstheoretischer Systeme(Hamburg, 1959), an unpublished doctoral diss.

4. Theodor Ackermann Antiquariat, Bibliothek Ernst Mach, 2 pts. (Munich, 1959–1960), a list of some 3,700 works from Mach’ working library.

5. K.D.Heller, Ernst Mach. Wegbereiter der modernen Physik. Mit ausgewählten Kapiteln aus seinem Werk (Vienna-New York, 1964).

6. Floyd Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (San Francisco, 1965), contains in English trans. Mach’ six papers one this subject (1865-1906).

7. Frank Kerkhof, ed., Symposium zum Anlass des 50 Todestages von Ernst Mach (Freiburg im Breisgau, 1966).

8. Erwin Hiebert, The Conception of Thermodynamics in the Scientific Thought of Mach and Planck(Freiburg im breisgau, 1968).

9. J.Hintikka, ed., “A Symposium on Ernst Mach,” in Synthese, 18 (1968), 132–301.

10. Joachim Thiele, ed.,Ernst Mach Abhandlungen: Die Geschichte und die Wurzel des satzes von der Erhaltung der Arbeit (1872). Zur Geschiche des Arbeitbegriffes (1873). Kultur und Mechanik (1915) (Amsterdam, 1969), a facs, ed. with forword and bibliography of Mach’ works.

11. Robert S.Cohen and R.J.Seeger eds.,Ernst Mach: Physicist and Philosopher, Boston Studies in the Philosophy of science, no. 6 (Dordrecht, 1970).

12. J.Bradley,Mach’s Phlosophy of Science (London, 1971).

13. John T.Blackmore, Ernst Mach. His Work, Life, and Influence (Berkeley, Calif., 1972).

Erwin N. Hiebert

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Ernst Mach

Ernst Mach

Ernst mach (1838-1916), an Austrian physicist and philosopher of science, made important contributions in several sciences but especially in the areas of the history and theory of science and of perception.

Ernst Mach was born on Feb. 18, 1838, in Turas in Moravia, then part of Austria and subsequently a province of the former Czechoslovakia. His father, Johann, was a high school teacher, and Ernst was tutored at home until he entered the University of Vienna, from which he graduated in 1860. In 1864 he became professor of mathematics at Graz; in 1867 he became professor of physics at Prague, a post he held until 1895, when he was appointed to the chair of the history and theory of the inductive sciences at Vienna. He was active in academic and political affairs, and after his retirement he was appointed to the upper house of the Austrian Parliament. He died near Munich on Feb. 19, 1916.

Mach is generally credited with establishing the study of the philosophy of sciences as a separate discipline. He brought to this study, in his words, "an incorruptible skepticism and independence." One of his most important works, The Science of Mechanics (1883), is an attack upon the "objective descriptions" of nature which in Newtonian physics produce such concepts as the "absolute" nature of space and time. Demonstration is a misplaced rigor which mistakes experiential summation for prediction. The relativism of his empiricism was an important corrective for modern science by its insistence that all concepts be traced to the objects to which they refer together with an explanation of the rules by which they are applied. For example, atomic theory is an explanation in physics and chemistry. But if such tools are taken to be unobservable realities rather than "theoretical models" for summarizing facts, then science has made the fatal error of identifying description with explanation.

Obviously Mach's views on the nature of science derived from his analysis of human knowledge. He acknowledged his indebtedness to the English empiricists, especially George Berkeley and David Hume. To him "the world consists only of our sensations," and this phenomenalism follows the empiricist tradition of deriving "ideas" from "impressions." Knowledge consists in communicating the observed distinctions of our sensations. From Mach's views has come the tradition of distinguishing between the public and private data of sensation, that is, that part of man's sensory experience which can be confirmed by others and man's individual perceptions. On this basis Mach proposed a unified theory of the sciences. The difference between physics and psychology, material and mental, is relative to the perspective of the observer. Color can be considered physically in terms of its dependencies or psychologically in terms of its receptivity. This scientific theory consists of coherent, concise descriptions of observed phenomena.

The Vienna Circle of contemporary positivism was originally founded as the Ernst Mach Society. Mach also gave his name to the Mach number, the standard scale for gradations of supersonic speed.

Further Reading

For discussions of Mach consult: Karl R. Popper, The Logic of Scientific Discovery (1935; trans. 1959); Carlton Berenda Weinberg, Mach's Empirio-pragmatism in Physical Science (1937); Richard Von Mises, Positivism: A Study in Human Understanding (1939; trans. 1951); Morris Raphael Cohen, Reason and Nature: An Essay on the Meaning of Scientific Method (1953); A. J. Ayer's introduction to his anthology, Logical Positivism (1959); and Brand Blanshard, Reason and Analysis (1962).

Additional Sources

Ernst Mach-a deeper look: documents and new perspectives, Dordrecht; Boston: Kluwer Academic Publishers, 1992. □

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Mach, Ernst

Ernst Mach (ĕrnst mäkh), 1838–1916, Austrian physicist and philosopher, b. Moravia. He taught (1864–67) mathematics at Graz and later, until his retirement in 1901, was professor of physics at Prague and Vienna. Mach, one of the leaders of modern positivism, did his major work in the philosophy of science. Following strictly empirical principles, he strove to rid science of all metaphysical and religious assumptions. He felt science should confine itself to the description of phenomena that could be perceived by the senses. This view challenged science's traditional claim of yielding absolute knowledge and was greatly influential in the development of logical positivism. Mach also did research in the field of ballistics; the Mach number is named for him. His works include Die Mechanik in ihrer Entwicklung (1883; tr. The Science of Mechanics, 1893); Die Analyse der Empfindungen (1886); Erkenntnis und Irrtum [perception and error] (1905).

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